Question

The statement “if \[{2^2} = 5\] , then I get first class“ is logically equivalent to
A. \[{2^2} = 5\]and I do not get first class
B. \[{2^2} = 5\]or I do not get first class
C. \[{2^2} \ne 5\] or I get first class
D. None of these

Answer 1

Hint: The term logically equivalent is the mathematical statement that can be used in place of other mathematical sentences. Here the above statement is in ‘if and then' type and we can convert it in other forms like contrapositive and converse. An example of a contrapositive statement is:- a number is divisible by 9 , then it is divisible by 3, so its contrapositive statement is; if a number is not divisible by 3 , it is not divisible by 9.

Complete step by step solution:
Let's break the statement into two parts- first one is A and second one is B.
A: \[{2^2} = 5\]
B: I get 1st class
Here is the mathematical representation of above if and then statement
\[(A \to B)\] And
Contrapositive statement of it is \[(B \to A)\]
 If I do not get first class, then \[{2^2} \ne 5\]
\[{2^2} \ne 5\] or I get first class.
Hence option (C) is correct.

Note: A proposition or theorem by contradicting both the subject and predicate or both the hypothesis and conclusion of a given proposition or theorem, and interchanging them “if not B then not A “is the contrapositive of “if A then B “. We apply this in the question above.